zinb.loglik.regression: Penalized log-likelihood of the ZINB regression model

In zinbwave: Zero-Inflated Negative Binomial Model for RNA-Seq Data

Description

This function computes the penalized log-likelihood of a ZINB regression model given a vector of counts.

Usage

zinb.loglik.regression(
  alpha,
  Y,
  A.mu = matrix(nrow = length(Y), ncol = 0),
  B.mu = matrix(nrow = length(Y), ncol = 0),
  C.mu = matrix(0, nrow = length(Y), ncol = 1),
  A.pi = matrix(nrow = length(Y), ncol = 0),
  B.pi = matrix(nrow = length(Y), ncol = 0),
  C.pi = matrix(0, nrow = length(Y), ncol = 1),
  C.theta = matrix(0, nrow = length(Y), ncol = 1),
  epsilon = 0
)

Arguments

alpha	the vectors of parameters c(a.mu, a.pi, b) concatenated
Y	the vector of counts
A.mu	matrix of the model (see Details, default=empty)
B.mu	matrix of the model (see Details, default=empty)
C.mu	matrix of the model (see Details, default=zero)
A.pi	matrix of the model (see Details, default=empty)
B.pi	matrix of the model (see Details, default=empty)
C.pi	matrix of the model (see Details, default=zero)
C.theta	matrix of the model (see Details, default=zero)
epsilon	regularization parameter. A vector of the same length as alpha if each coordinate of alpha has a specific regularization, or just a scalar is the regularization is the same for all coordinates of alpha. Default=O.

Details

The regression model is parametrized as follows:

log(μ) = A_μ * a_μ + B_μ * b + C_μ

logit(Π) = A_π * a_π + B_π * b

log(θ) = C_θ

where μ, Π, θ are respectively the vector of mean parameters of the NB distribution, the vector of probabilities of the zero component, and the vector of inverse dispersion parameters. Note that the b vector is shared between the mean of the negative binomial and the probability of zero. The log-likelihood of a vector of parameters α = (a_μ; a_π; b) is penalized by a regularization term ε ||α||^2 / 2 is ε is a scalar, or ∑_{i}ε_i α_i^2 / 2 is ε is a vector of the same size as α to allow for differential regularization among the parameters.

Value

the penalized log-likelihood.

zinbwave documentation built on Nov. 8, 2020, 8:11 p.m.